Year 12 Math Question Paper

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Revision Year 12 Maths B, Term 4 1. The function, y=3cosx+5 has an amplitude of 3 and a mean value of 5. Using these values, the range can be found to be 2≤y≤8 . Find the range of the function y=4cosx+7 2. Find the exact value of tan600 (Hint, draw a standard triangle to help) 3. The -coordinate of the stationary point of a function can be found by following these steps: * differentiate the function * let the derivative = 0 * solve for Find the -coordinate of the stationary point of the function, 4. Fully simplify: 3sin2θ+5cos2θ 5. A copper mine produces t tonnes of copper each week at a total cost of $C given by: Ct=1000 -70t+5t2 . How many tonnes of copper are needed to be…show more content…
Using algebraic methods, find the value for x which will give the greatest area. 2 In a West Queensland town on a day in the middle of winter, the temperature (T) in degrees Celsius is modelled by the function: T=16-8cosπx12, where x is the number of hours since 6 am. Lynne refuses to leave her nice warm house until the temperature has risen to 12º C. What is the earliest time she can leave? 3. Fully simplify the expression, tanx1+ tan2x . Use the knowledge that sin x= -35 and π2≤x ≤ 3π2 to express your simplified expression as an exact answer in fraction form. 4 Heat loss from electric hot water systems is an environmental issue. It is recognised that the heat loss from a closed, full hot water tank is proportional to the surface area of the tank. Determine the ratio of the heat loss from a 1m3 cylindrical tank of optimum dimensions (that is, the dimensions of the cylindrical tank for which the heat loss is a minimum) to the heat loss from a cubic tank with the same volume. Which tank design do you recommend as being more “environmentally friendly”? Remember: Vcylinder= πr2h SA cylinder= 2πr2+

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